I suffer from absentmindedness and constant worries during prayer, what should I do?
You should take refuge in Allah from the whispers of the devil and life worries. You should also seek Allah`s help and offer a lot of Istigfar (seeking the forgiveness of Allah). And Allah Knows Best.
Is Iddah (waiting period) incumbent on an old woman whose husband had died?
Upon the death of the husband, Iddah is incumbent on the wife regardless of their age. And Allah Knows Best.
What is the ruling on having brotherly ties between a strange man and a strange woman, and is the former considered a Mahram (unmarriageable) to the latter?
Such a relation between a strange man and a strange woman is forbidden in Islam because it involves forbidding what Allah has allowed by marriage, and allowing what Allah has forbidden such as looking and the like. Such a relation doesn`t render any act lawful between them, thus they are forbidden to look at each other, have a Khulwah (seclusion), and travel together.
What is the ruling on taking part in an online contest to win a prize of 100,000 dollars in return for answering thirty questions in different fields of knowledge and science? Knowing that there is no drawing of lots; only one or two cards are purchased to commence the contest.
Praise be to Allah the Lord of the Worlds. May His peace and blessings be upon our Prophet Mohammad and upon all his family and companions.
This is a form of gambling, which is impermissible to participate in, because the people in charge of this online contest increase the value of the calls to compensate for the value of the prizes. And Allah The Almighty Knows Best.